Lines of minima in outer space

Lines of Minima with No End in Thurston’s Boundary of Teichmüller Space

Let ν+ and ν− be two measured laminations which fill up a hyperbolic surface. Kerckhoff [Duke Math. J. 65 (1992), 187–213] defines a line of minima as a family of surfaces where convex combinations of the hyperbolic length functions of ν+ and ν− are minimum. This is a proper curve in the Teichmüller space. We show that there exists a line of minima which does not converge in the Thurston compac...

Plants circling in outer space

Plants do not grow in a strict linear manner, rather they circumnutate. That is, they exhibit an oscillatory or helical growth pattern around an axis. Circumnutation is readily apparent in vines such as morning glory or grape (Fig. 1), but in fact it is nearly ubiquitous in plants. Circumnutation occurs in almost all plant organs throughout all stages of development (Johnsson, 1997; Larson, 200...

Developmental Biology in Outer Space

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Contracting orbits in Outer space

We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestvina– Feighn, and is used to give conditions for when a subgroup of Out(F) has a quasi-isometric orbit map into the free factor complex. It also allows one to construct many new examples of strongly contracting geodesi...

Plants circling in outer space.